A method for extracting frequency domain impedance characteristics of grounding grid under intermediate frequency oscillation impact

Abstract

The present application provides a kind of method for extracting the frequency domain impedance characteristics of grounding grid under the impact of intermediate frequency oscillation, belongs to the technical field of grounding grid operation and maintenance, the present application establishes the three-dimensional geometric model of grounding grid and uses the fractal dimension adaptive grid generation algorithm to divide the grid in the conductor area, establishes the multi-layer soil complex permittivity model to characterize the frequency variation characteristics of soil electromagnetic parameters, decomposes the intermediate frequency impact excitation signal into multiple narrowband components and inputs the artificial intelligence impedance characteristic extraction model based on neural tangent kernel theory, calculates the current density distribution and electromagnetic field distribution under different frequency points, extracts the skin effect depth and adjacent effect coupling coefficient, constructs the frequency response function of grounding grid and identifies the distribution position of resonance frequency point, adaptively adjusts the grid density parameters and iterative convergence precision parameters according to the ionization degree of soil, solves the problem that the frequency domain impedance characteristics of grounding grid under the condition of intermediate frequency impact are difficult to accurately extract.

Description

Technical Field

[0001] This invention belongs to the field of grounding grid operation and maintenance technology, and specifically relates to a method for extracting the frequency domain impedance characteristics of a grounding grid under medium-frequency oscillation impact. Background Technology

[0002] As a crucial safety facility in power systems, the impedance characteristics of the grounding grid under medium-frequency impulses directly affect the system's transient safety performance. Traditional grounding grid impedance characteristic analysis primarily relies on the finite element method or the finite-difference time-domain method to numerically solve the electromagnetic field. This involves establishing a three-dimensional model of the grounding grid and setting boundary conditions to calculate the current and potential distributions under a given excitation, thereby extracting impedance parameters. However, under medium-frequency impulse excitation, significant skin and proximity effects exist within the grounding grid conductors, leading to strong spatial non-uniformity in current density distribution. Traditional uniform mesh generation methods struggle to balance computational accuracy and efficiency. In geometrically complex regions such as conductor bends and branch nodes, excessively sparse meshes increase solution errors, while overly dense meshes in regions with gentle electric fields waste computational resources. Furthermore, the frequency-dependent variation of soil electromagnetic parameters and the impact of soil ionization on impedance characteristics are difficult to accurately characterize. Traditional methods suffer from high model complexity and poor computational convergence when dealing with multi-frequency coupling and nonlinear effects. In other words, existing technologies face the technical challenge of accurately extracting the frequency-domain impedance characteristics of the grounding grid under medium-frequency impulse conditions. Summary of the Invention

[0003] In view of this, the present invention provides a method for extracting the frequency domain impedance characteristics of a grounding grid under medium-frequency oscillation impact, which can solve the technical problem in the prior art that it is difficult to accurately extract the frequency domain impedance characteristics of a grounding grid under medium-frequency impact conditions.

[0004] This invention is implemented as follows: A method for extracting the frequency domain impedance characteristics of a grounding grid under mid-frequency oscillation impulse includes the following steps: establishing a three-dimensional geometric model of the grounding grid; defining the spatial coordinates of the horizontal and vertical grounding bodies; collecting the conductor radius, vertical grounding body length, and horizontal grounding body length of the grounding grid; using a fractal dimension adaptive grid generation algorithm to divide the conductor region of the grounding grid into grids and obtain initial grid density parameters; collecting spatial distribution data of soil resistivity and soil permeability in the area where the grounding grid is located; establishing a multi-layer soil complex dielectric constant model; obtaining the frequency variation parameters of soil resistivity and soil dielectric constant at different depths; setting the frequency range of the mid-frequency impulse excitation signal to 0.5kHz to 10kHz; decomposing the mid-frequency impulse excitation signal into multiple narrowband components; and inputting the conductor radius, vertical grounding body length, horizontal grounding body length, soil resistivity frequency variation parameters, and soil dielectric constant frequency variation parameters into the impedance characteristics. The model is extracted, and the current density vector field distribution and electromagnetic field distribution inside the grounding grid conductor at different frequency points are calculated through the impedance characteristic extraction model. Based on Maxwell's equations, the spatial variation law of current density in the cross section of the grounding grid conductor is solved. The skin effect depth and proximity effect coupling coefficient are extracted according to the current density vector field distribution. The frequency-varying components of equivalent resistance and equivalent inductance at different frequency points are calculated, and the real part and imaginary part of the frequency-domain impedance of the grounding grid are obtained. The frequency response function of the grounding grid is constructed based on the real part and imaginary part of the frequency-domain impedance of the grounding grid, and the distribution location of the resonant frequency points in the frequency response function is identified. The frequency-domain response of different narrowband components is synthesized into a time-domain impulse response using the convolution theorem. The local electric field strength and current density peak value are collected, the soil ionization degree is calculated, and the soil ionization degree, current density peak value and local electric field strength are input into an adaptive adjustment function. The initial grid density parameter and iterative convergence accuracy parameter are adjusted according to the adjustment value.

[0005] The fractal dimension adaptive grid generation algorithm densifies the grid cells at conductor bends and branch nodes, and sparses the grid cells in regions with gentle electric field distribution. It quantifies the spatial complexity by calculating the box dimension and information dimension of the grounding grid geometry at different observation scales.

[0006] The box dimension reflects the filling characteristics of the grounding grid conductor in space, the information dimension reflects the non-uniformity of the grounding grid node distribution, and the grid density of the region is automatically determined based on the size of the local fractal dimension value.

[0007] The fractal dimension adaptive mesh generation algorithm uses a quadtree data structure to hierarchically manage the two-dimensional cross-sectional mesh and an octree data structure to hierarchically manage the three-dimensional spatial mesh. It achieves dynamic generation and optimization of multi-level meshes through recursive subdivision.

[0008] The specific implementation steps of the fractal dimension adaptive mesh generation algorithm include: projecting the three-dimensional geometric model of the grounding grid onto the horizontal and vertical planes, covering the grounding grid conductor with cubic boxes of decreasing side lengths at different scales, counting the minimum number of boxes required at each scale, and calculating the box dimension by using the minimum number of boxes and the slope of the box scale in the double logarithmic coordinate system.

[0009] The fractal dimension adaptive grid generation algorithm assigns a probability measure to each node of the grounding grid to characterize the concentration of current distribution, calculates the information dimension to quantify the non-uniformity of node distribution, and performs quadtree or octree recursive subdivision of the coarse grid cells when the fractal dimension exceeds a set threshold.

[0010] The multilayer soil complex dielectric constant model characterizes the soil dielectric constant and soil conductivity as functions of frequency, and represents the electromagnetic properties of the soil as a frequency-dependent complex number. The real part of the complex dielectric constant corresponds to the soil dielectric constant, and the imaginary part of the complex dielectric constant corresponds to the ratio of soil conductivity to frequency.

[0011] The multilayer soil complex dielectric constant model describes the dispersion characteristics of soil dielectric constant with frequency using the Debye relaxation model or the Cole-Cole model.

[0012] In this process, a corresponding frequency domain excitation source is established for each narrowband component. The impedance characteristic extraction model utilizes the connection between the infinite width limit theory based on the neural tangent kernel and the Gaussian process. By analyzing the neural network as equivalent to the kernel method under infinite width, the neural tangent kernel is used for theoretical analysis and uncertainty quantification.

[0013] The specific structure of the impedance characteristic extraction model is as follows: the input layer receives the grounding grid conductor radius, vertical grounding body length, horizontal grounding body length, soil resistivity frequency variation parameters, soil dielectric constant frequency variation parameters, and excitation frequency; feature extraction and nonlinear mapping are performed through three hidden layers; and the output layer outputs the real part of the grounding grid frequency domain impedance, the imaginary part of the grounding grid frequency domain impedance, and the current density distribution correction coefficient.

[0014] The steps for establishing the training dataset for the impedance characteristic extraction model include: using the finite element method to perform electromagnetic field simulations on grounding grids with different topologies in the frequency range of 0.5kHz to 10kHz, obtaining the equivalent impedance and current density distribution of the grounding grid at different frequency points, and changing the soil resistivity from 10... Up to 1000 Generate sample data covering different working conditions.

[0015] The impedance characteristic extraction model training uses the Xavier initialization method to initialize the network weights, uses mean squared error as the loss function, and uses the Adam optimizer for gradient descent updates. During training, the neural tangent kernel matrix of each layer is recorded, and the training dynamics of the network are analyzed through the eigenvalues ​​of the neural tangent kernel matrix.

[0016] The principle of connecting the infinite width limit theory based on the neural tangent kernel with the Gaussian process is that when the width of the neural network approaches infinity, the output of the network under random initialization conditions is equivalent to a Gaussian process, and its kernel function is the neural tangent kernel. The training process is equivalent to performing kernel ridge regression in the regenerating kernel Hilbert space defined by the neural tangent kernel.

[0017] The skin effect depth refers to the depth value at which the current density inside the conductor of the grounding grid decreases exponentially with increasing depth from the surface under the action of high-frequency current. The skin effect depth is inversely proportional to the square root of the excitation frequency.

[0018] The proximity effect coupling coefficient is a parameter that quantifies the electromagnetic coupling strength between adjacent conductors. When multiple conductors are arranged in parallel and carry high-frequency current, the alternating magnetic field generated by each conductor will induce eddy currents in the adjacent conductors. The proximity effect coupling coefficient is calculated using the conductor spacing, the radius of the grounding grid conductor, and the excitation frequency.

[0019] The grounding grid frequency response function calculates the equivalent impedance modulus and impedance phase characteristics of the grounding grid, establishes the mapping relationship between the intermediate frequency impulse excitation frequency and the real part and imaginary part of the frequency domain impedance of the grounding grid, and the grounding grid frequency response function is a complex function that describes the variation of the grounding grid impedance with the excitation frequency.

[0020] The resonant frequency point distribution location refers to the frequency location where the frequency response function of the grounding grid exhibits an extreme value. At the resonant frequency point distribution location, the inductive impedance and capacitive impedance of the grounding grid cancel each other out, resulting in a minimum or maximum value of the total impedance. The resonant frequency point distribution location is jointly determined by the geometric dimensions of the grounding grid and the electromagnetic parameters of the soil.

[0021] The adaptive adjustment function calculates the adjustment value. When the adjustment value a∈[0, 0.3), the initial grid density parameter is maintained. When the adjustment value a∈[0.3, 0.7), the initial grid density parameter is increased by 20%. When the adjustment value a∈[0.7, 1], the initial grid density parameter is increased by 50% and the iterative convergence accuracy parameter is reduced.

[0022] The degree of soil ionization refers to the extent to which the local conductivity increases sharply due to the ionization of gas or liquid in the soil under the action of a strong electric field. The degree of soil ionization is quantified by the ratio of the local electric field strength to the soil breakdown field strength. When the local electric field strength approaches or exceeds the breakdown field strength, the degree of soil ionization increases.

[0023] This invention proposes a method for extracting the frequency domain impedance characteristics of grounding grids based on fractal dimension adaptive meshes and neural tangent kernel theory. The method automatically adjusts the mesh density according to the local complexity of the grounding grid's geometry using a fractal dimension adaptive mesh generation algorithm. Mesh density is automatically increased at conductor bends and branch nodes where electromagnetic fields change drastically, while maintaining a sparse mesh in areas with gentle electric field distribution. This allows computational resources to be precisely allocated to key areas, resolving the contradiction of insufficient accuracy or excessive computational cost when using traditional uniform meshes to handle multi-scale geometric features. This invention establishes a multi-layer soil complex permittivity frequency-varying model and constructs an impedance characteristic extraction model based on neural tangent kernel theory. The training process of a deep neural network is mapped to a linear optimization problem using kernel methods, which is equivalent to a Gaussian process in the infinite-width limit. This provides a rigorous theoretical convergence guarantee and uncertainty quantification capability for impedance prediction. Even when facing grounding grid configurations not fully covered in the training dataset, it can still provide reliable impedance predictions and confidence interval estimates, avoiding the risk of inaccurate predictions in extrapolation cases of traditional black-box neural networks. In summary, this invention solves the technical problem of accurately extracting the frequency domain impedance characteristics of grounding grids under mid-frequency impulse conditions. Attached Figure Description

[0024] Figure 1 This is a flowchart of the method of the present invention.

[0025] Figure 2 This is a schematic diagram of the data acquisition system.

[0026] Figure 3 This is a graph of the frequency response function of the grounding grid.

[0027] Figure 4 This is a time-domain waveform diagram of the grounding grid's impulse response.

[0028] Figure 5 This is a distribution map of adjustment values ​​in different regions. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0030] like Figure 1 The diagram shows a flowchart of a method for extracting the frequency domain impedance characteristics of a grounding grid under medium-frequency oscillation impulse, provided by the present invention. This method includes the following steps: S01. Establish a three-dimensional geometric model of the grounding grid, define the spatial coordinates of the horizontal and vertical grounding bodies, collect the conductor radius, vertical grounding body length and horizontal grounding body length of the grounding grid, use the fractal dimension adaptive grid generation algorithm to divide the conductor area of ​​the grounding grid into grids, densify the grid cells at conductor bends and branch nodes, and sparse the grid cells in areas with gentle electric field distribution to obtain the initial grid density parameters. S02. Collect spatial distribution data of soil resistivity and soil magnetic permeability in the area where the grounding grid is located, establish a multi-layer soil complex dielectric constant model, characterize the soil dielectric constant and soil conductivity as functions of frequency, and obtain the frequency-varying parameters of soil resistivity and soil dielectric constant at different depths. S03. Set the frequency range of the intermediate frequency impulse excitation signal to 0.5kHz to 10kHz, decompose the intermediate frequency impulse excitation signal into multiple narrowband components, establish a corresponding frequency domain excitation source for each narrowband component, and input the frequency-varying parameters of the grounding grid conductor radius, vertical grounding body length, horizontal grounding body length, soil resistivity, and soil dielectric constant into the impedance characteristic extraction model. Calculate the current density vector field distribution and electromagnetic field distribution inside the grounding grid conductor at different frequency points using the impedance characteristic extraction model. S04. Solve the spatial variation law of current density in the conductor cross section of the grounding grid based on Maxwell's equations. Extract the skin effect depth and proximity effect coupling coefficient according to the current density vector field distribution. Calculate the frequency-varying components of equivalent resistance and equivalent inductance at different frequency points to obtain the real part and imaginary part of the frequency domain impedance of the grounding grid. S05. Construct the frequency response function of the grounding grid based on the real part and the imaginary part of the frequency domain impedance of the grounding grid, identify the distribution of resonant frequency points in the frequency response function of the grounding grid, calculate the equivalent impedance modulus and the impedance phase characteristics of the grounding grid, and establish the mapping relationship between the intermediate frequency impulse excitation frequency and the real part and the imaginary part of the frequency domain impedance of the grounding grid. S06. Using the convolution theorem, the frequency domain responses of different narrowband components are synthesized into a time domain impulse response. Local electric field strength and current density peak values ​​are collected, and the soil ionization degree is calculated. The soil ionization degree, current density peak value, and local electric field strength are input into an adaptive adjustment function. The adjustment value is calculated through the adaptive adjustment function. The initial grid density parameter and the iteration convergence accuracy parameter are adjusted according to the adjustment value. When the adjustment value a∈[0, 0.3), the initial grid density parameter is maintained. When the adjustment value a∈[0.3, 0.7), the initial grid density parameter is increased by 20%. When the adjustment value a∈[0.7, 1], the initial grid density parameter is increased by 50% and the iteration convergence accuracy parameter is reduced.

[0031] The principle of the fractal dimension adaptive mesh generation algorithm is to quantify the spatial complexity of the grounding grid geometry by calculating the box dimension and information dimension at different observation scales. The box dimension reflects the filling characteristics of the grounding grid conductor in space, and the information dimension reflects the non-uniformity of the grounding grid node distribution. The mesh densification degree of the region is automatically determined according to the magnitude of the local fractal dimension value. A quadtree data structure is used to hierarchically manage the two-dimensional cross-sectional mesh, and an octree data structure is used to hierarchically manage the three-dimensional spatial mesh. At conductor bends and branch nodes, the local fractal dimension increases due to geometric abrupt changes, thereby triggering automatic mesh densification. In regions with a gentle electric field distribution, the mesh remains sparse due to the smaller fractal dimension. The dynamic generation and optimization of multi-level meshes are achieved through recursive subdivision.

[0032] The specific implementation steps of the fractal dimension adaptive mesh generation algorithm include: projecting the three-dimensional geometric model of the grounding grid onto the horizontal and vertical planes; covering the grounding grid conductor with cubes of decreasing side length at different scales; calculating the minimum number of boxes required at each scale; calculating the box dimension by the slope of the minimum number of boxes and the box scale in a double logarithmic coordinate system; assigning a probability measure to each node of the grounding grid to characterize the concentration of current distribution; calculating the information dimension to quantify the non-uniformity of node distribution; initializing the entire computational region as a coarse grid; traversing each coarse grid cell to calculate the local fractal dimension of the grounding grid conductor portion it contains; when the local fractal dimension exceeds a set threshold, recursively subdividing the coarse grid cell using a quadtree or octree; repeating the subdivision process until the grid density meets the requirements of the local fractal dimension or reaches the preset maximum subdivision level; and finally forming an adaptive grid that is dense in complex regions and sparse in simple regions.

[0033] The fractal dimension adaptive mesh generation algorithm establishes a quantitative correlation between the geometric complexity of the grounding grid and the mesh density, enabling computational resources to be concentrated in areas with drastic electromagnetic field changes. This avoids generating redundant mesh cells in areas with gentle electric fields, thereby significantly reducing the total number of meshes and computation time while ensuring the accuracy of current density calculation. For grounding grid structures with a large number of branches and bends, the fractal dimension adaptive mesh generation algorithm can automatically identify and prioritize the densification of key areas, resolving the contradiction between insufficient accuracy or excessive computational load of traditional uniform meshes when processing multi-scale geometric features.

[0034] The multilayer soil complex permittivity model characterizes the electromagnetic properties of soil as a frequency-dependent complex number. The real part of the complex permittivity corresponds to the soil permittivity, and the imaginary part corresponds to the ratio of soil conductivity to frequency. The dispersion characteristics of the soil permittivity with frequency are described by the Debye relaxation model or the Cole-Cole model. Frequency-varying parameter fitting curves are established by measuring the permittivity and conductivity of the soil at different frequencies. For multilayer soil structures, frequency-varying models of the complex permittivity of each layer need to be established separately, and the boundary conditions of the interlayer interfaces need to be defined.

[0035] The specific structure of the impedance characteristic extraction model is as follows: the input layer receives the conductor radius of the grounding grid, the length of the vertical grounding body, the length of the horizontal grounding body, the frequency-varying parameters of soil resistivity and soil dielectric constant, and the excitation frequency. Feature extraction and nonlinear mapping are performed through three hidden layers. The first hidden layer has 128 neurons to extract the spatial topological features of the grounding grid. The second hidden layer has 256 neurons to fuse soil parameters and frequency information. The third hidden layer has 128 neurons to construct a high-dimensional representation of the impedance characteristics. The output layer outputs the real part and imaginary part of the frequency domain impedance of the grounding grid, as well as the current density distribution correction coefficient. The impedance characteristic extraction model utilizes the infinite width limit theory based on neural tangent kernels and the connection of Gaussian processes. By analyzing that the neural network is equivalent to the kernel method under infinite width, the neural tangent kernel is used for theoretical analysis and uncertainty quantification, while retaining the practical training advantages of finite width networks.

[0036] The steps for establishing the training dataset for the impedance characteristic extraction model specifically include: using the finite element method to perform electromagnetic field simulations on grounding grids with different topologies in the frequency range of 0.5kHz to 10kHz, obtaining the equivalent impedance and current density distribution of the grounding grid at different frequency points, and changing the soil resistivity from 10... Up to 1000 By changing the conductor radius of the grounding grid from 5mm to 20mm and the length of the vertical grounding electrode from 1m to 10m, sample data covering different working conditions are generated. Each sample includes the conductor radius of the grounding grid, the length of the vertical grounding electrode, the length of the horizontal grounding electrode, the frequency-varying parameters of soil resistivity and soil dielectric constant, and the excitation frequency as input features. The real part and imaginary part of the frequency-domain impedance of the grounding grid and the current density distribution are included as output labels. The sample data are divided into training set and validation set in an 8:2 ratio.

[0037] The specific steps for training the impedance characteristic extraction model include: initializing the network weights using the Xavier initialization method, using mean squared error as the loss function to measure the deviation between the predicted impedance and the true impedance, using the Adam optimizer for gradient descent updates, setting the learning rate to 0.001, the batch size to 32, and the number of training epochs to 200, recording the neural tangent kernel matrix of each layer during training, analyzing the network's training dynamics through the eigenvalues ​​of the neural tangent kernel matrix, triggering an early stopping mechanism when the validation set loss does not decrease for 10 consecutive epochs, and saving the model weights with the minimum validation set loss as the final model.

[0038] The principle of the connection between the infinite width limit theory of neural tangent kernels and Gaussian processes is that when the width of the neural network approaches infinity, the output of the network under random initialization conditions is equivalent to a Gaussian process, whose kernel function is the neural tangent kernel. The neural tangent kernel describes the inner product between the gradients of the network parameters. During training, the neural tangent kernel remains approximately invariant, making the training dynamics of the network linearized under the infinite width limit. Thus, the training process is equivalent to performing kernel ridge regression in the regenerating kernel Hilbert space defined by the neural tangent kernel. This connection makes the training and generalization performance of the neural network interpretable and theoretically guaranteed.

[0039] The mechanism maps the training process of a deep neural network to a linear optimization problem of a kernel method, providing a rigorous theoretical convergence guarantee and uncertainty quantification capability for the impedance characteristic extraction model. This enables the impedance characteristic extraction model to provide reliable impedance predictions and confidence interval estimates even when facing grounding grid configurations that are not fully covered in the training dataset. As a result, the accuracy and robustness of grounding system performance evaluation under medium-frequency impulse conditions are improved, and the risk of inaccurate predictions in extrapolation cases of traditional black-box neural networks is avoided.

[0040] The skin effect depth refers to the depth value corresponding to the exponential decay of the current density inside the conductor of the grounding grid under the action of high-frequency current, which decreases with increasing depth from the surface. The skin effect depth is inversely proportional to the square root of the excitation frequency and is related to the resistivity and permeability of the conductor. In the mid-frequency range, the skin effect causes the current to concentrate in a thin layer on the surface of the conductor, which reduces the effective cross-sectional area of ​​the conductor and increases the equivalent resistance.

[0041] The proximity effect coupling coefficient is a parameter that quantifies the electromagnetic coupling strength between adjacent conductors. When multiple conductors are arranged in parallel and carry high-frequency current, the alternating magnetic field generated by each conductor will induce eddy currents in the adjacent conductors. The eddy currents change the current distribution in the original conductors. The proximity effect coupling coefficient is calculated by the conductor spacing, the radius of the grounding grid conductor, and the excitation frequency, and reflects the degree of influence of adjacent conductors on each other's impedance characteristics.

[0042] The frequency-varying component of the equivalent resistance is the incremental part of the equivalent resistance of the grounding grid as the excitation frequency changes. It is caused by the skin effect and the proximity effect. At low frequencies, the equivalent resistance is close to the DC resistance. As the excitation frequency increases, the equivalent resistance increases due to the decrease in the effective conductive cross-sectional area. The frequency-varying component of the equivalent resistance is obtained by calculating the power loss on the conductor by integrating the current density and then dividing by the square of the current.

[0043] The frequency-varying component of the equivalent inductance is the part of the grounding grid that changes with the excitation frequency. It is caused by the change in the distribution of the magnetic field inside the conductor due to the skin effect. At low frequencies, the magnetic field is uniformly distributed inside the conductor. As the excitation frequency increases, the magnetic field gradually concentrates near the surface of the conductor, resulting in a decrease in the internal inductance while the external inductance remains stable. The frequency-varying component of the equivalent inductance affects the inductive impedance and phase characteristics of the grounding grid.

[0044] The grounding grid frequency response function is a complex function that describes the variation of the grounding grid impedance with the excitation frequency. The magnitude of the grounding grid frequency response function represents the change of the impedance amplitude with the excitation frequency, and the phase of the grounding grid frequency response function represents the change of the phase difference between voltage and current with the excitation frequency. The resonant frequency point and anti-resonant frequency point of the grounding grid can be identified by plotting the amplitude-frequency curve and phase-frequency curve of the grounding grid frequency response function.

[0045] The resonant frequency distribution location refers to the frequency location where the frequency response function of the grounding grid exhibits an extreme value. At the resonant frequency distribution location, the inductive impedance and capacitive impedance of the grounding grid cancel each other out, resulting in a minimum or maximum value in the total impedance. The resonant frequency distribution location is jointly determined by the geometric dimensions of the grounding grid and the electromagnetic parameters of the soil. If a resonant frequency distribution location exists in the frequency components included in the medium-frequency impulse excitation, the impedance characteristics of the grounding grid will change significantly.

[0046] The adaptive adjustment function calculates the adjustment value based on the soil ionization degree, peak current density, and local electric field strength. The adjustment value is obtained by weighting the normalized soil ionization degree to the range of 0 to 1 with the normalized value of the peak current density and the normalized value of the local electric field strength, with weighting coefficients of 0.5, 0.3, and 0.2, respectively. The adaptive adjustment function is used to dynamically adjust the initial grid density parameter and the iteration convergence accuracy parameter. When the adjustment value is small, it indicates that the soil ionization degree is weak, and the initial grid density parameter is maintained. When the adjustment value is medium, the initial grid density parameter is moderately increased to capture the impedance nonlinear change caused by ionization. When the adjustment value is large, the initial grid density parameter is significantly increased and the iteration convergence accuracy parameter is reduced to accurately simulate the impedance characteristics under strong ionization conditions.

[0047] The degree of soil ionization refers to the extent to which the local conductivity increases sharply due to the ionization of gas or liquid in the soil under the action of a strong electric field. The degree of soil ionization is quantified by the ratio of the local electric field strength to the soil breakdown field strength. When the local electric field strength approaches or exceeds the breakdown field strength, the degree of soil ionization increases, and the resistivity of the ionized soil decreases significantly, affecting the impedance characteristics and current distribution of the grounding grid.

[0048] The initial grid density parameter refers to the number of grid cells divided within a unit volume of space. The initial grid density parameter directly affects the spatial resolution and computational accuracy of electromagnetic field solutions. In regions with large current density gradients or drastic changes in local electric field intensity, a higher initial grid density parameter is required to accurately capture the spatial changes of physical quantities. In regions with gentle electromagnetic field distribution, a lower initial grid density parameter is used to save computational resources.

[0049] The iteration convergence accuracy parameter is the threshold for judging whether the iteration has converged during the numerical solution process. When the relative error between two adjacent iterations is less than the iteration convergence accuracy parameter, the solution is considered to have converged. A smaller iteration convergence accuracy parameter can obtain higher solution accuracy but requires more iterations and computation time. When the soil ionization degree is significant, the iteration convergence accuracy parameter needs to be reduced to ensure the reliability of the numerical solution.

[0050] As an optional implementation, the present invention also provides a computer-based method for forming a grounding grid frequency domain impedance characteristic extraction system under medium-frequency oscillation impact, wherein the computer is provided with a readable storage medium storing program instructions, and the program instructions execute the above-described method when running in the computer.

[0051] The specific implementation methods of the above steps are described in detail below.

[0052] The specific implementation of step S01 is as follows: First, spatial coordinate data of the grounding grid is obtained through on-site measurement. A total station or RTK positioning device is used to record the three-dimensional coordinate points of the horizontal and vertical grounding electrodes, establishing the geometric topology of the grounding grid. The radius of the grounding grid conductor and the lengths of the vertical and horizontal grounding electrodes are measured and recorded. After completing the geometric modeling, a fractal dimension adaptive mesh generation algorithm is initiated. First, the three-dimensional geometric model of the grounding grid is projected onto the horizontal and vertical planes. The box counting method is used to count the minimum number of cubic boxes required to cover the grounding grid conductor at different observation scales. The box dimension is obtained by fitting a straight line between the minimum number of boxes and the box side length in a double logarithmic coordinate system and calculating the slope. The box dimension reflects the spatial filling characteristics of the grounding grid conductor. Next, a probability measure is assigned to each node of the grounding grid. The probability measure is determined by the ratio of the predicted current density at the node to the total current. The information dimension is calculated to quantify the non-uniformity of the node distribution. The information dimension is obtained through the scaling relationship of the Shannon entropy of the probability measure at different scales. The entire computational domain is initialized as a coarse grid. Each coarse grid cell is traversed and the local fractal dimension of the grounding grid conductor portion it contains is calculated. When the local fractal dimension exceeds the threshold of 1.5, a quadtree or octree recursive subdivision is triggered. The recursive subdivision process continues until the grid density meets the requirements of the local fractal dimension or reaches the preset maximum subdivision level of 6 layers. Finally, an adaptive grid is formed that is dense at conductor bends and branch nodes and sparse in areas with a gentle electric field distribution. The initial grid density parameters are obtained as the spatial discretization basis for subsequent electromagnetic field solutions.

[0053] The specific implementation of step S02 involves arranging multiple measurement points in the grounding grid area to conduct stratified soil resistivity testing. The spatial distribution data of soil resistivity at different depths is measured using the Winner quadrupole method or the Schlumberger method. The measurement depth ranges from the ground surface to 2m below the end of the vertical grounding electrode. The spacing between measurement points is determined according to the size of the grounding grid, typically 5m to 10m. Simultaneously, a magnetic susceptibility meter is used to measure the spatial distribution data of soil magnetic permeability, establishing a soil stratification model and determining the thickness and resistivity of each layer. A multilayer soil complex dielectric constant model is established based on the Debye relaxation model. This model describes the dispersion characteristics of the soil dielectric constant with frequency and includes three parameters: static dielectric constant, high-frequency limiting dielectric constant, and relaxation time constant. Frequency-varying parameter fitting curves are established by measuring the dielectric constant and conductivity of soil samples at different frequencies. For multi-layered soil structures, frequency-varying models of the complex permittivity of each layer are established. The real part of the complex permittivity corresponds to the soil permittivity, and the imaginary part corresponds to the ratio of soil conductivity to frequency. Boundary conditions are defined for the continuity of the tangential component of the electric field and the normal component of the electric displacement at the interlayer interface. Finally, frequency-varying parameters of soil resistivity and soil permittivity at different depths are obtained for subsequent impedance calculations.

[0054] The specific implementation of step S03 involves using a Fast Fourier Transform (FFT) to decompose the time-domain signal into a frequency-domain representation based on the time-domain waveform of the intermediate-frequency impulse excitation signal. Spectral components within the frequency range of 0.5 kHz to 10 kHz are extracted, and these spectral components are divided into multiple narrowband components at 2 kHz intervals. Each narrowband component corresponds to a center frequency and amplitude. A corresponding frequency-domain excitation source is established for each narrowband component. The frequency-varying parameters of the grounding grid conductor radius, vertical and horizontal grounding electrode lengths, soil resistivity, and soil dielectric constant, along with the excitation frequency of the current narrowband component, are used as input features and input to the input layer of the impedance characteristic extraction model. The impedance characteristic extraction model extracts the spatial topological features of the grounding grid through the first hidden layer, including the connection relationship between conductors and the node distribution density. The second hidden layer nonlinearly fuses soil parameters and frequency information to capture the coupling effect of frequency changes in soil resistivity and dielectric constant on impedance. The third hidden layer constructs a high-dimensional representation of the impedance characteristics. Finally, the output layer generates the current density vector field distribution and electromagnetic field distribution inside the grounding grid conductors at different frequency points. The current density vector field distribution includes the magnitude and direction of the current density in each grid cell, and the electromagnetic field distribution includes the spatial distribution of electric field strength and magnetic field strength.

[0055] The specific implementation of step S04 is to establish the partial differential equations of the electromagnetic field of the grounding grid based on Maxwell's equations, and to discretize and solve the partial differential equations using the finite element method. The adaptive mesh generated in step S01 is used to spatially discretize the grounding grid conductor and its surrounding soil region. Shape functions are established within each mesh element, and the overall stiffness matrix and overall load vector are assembled. The potential distribution at the nodes is obtained by iteratively solving the linear equations, and the electric field distribution is obtained by calculating the gradient of the potential distribution. The spatial variation law of the current density across the grounding grid conductor cross-section is calculated according to Ohm's law. The skin effect depth is extracted from the current density vector field distribution. By calculating the decay curve of the current density with depth from the conductor surface, the depth value corresponding to the current density decaying to 36.8% of the surface current density is determined. The skin effect depth is inversely proportional to the square root of the excitation frequency. Simultaneously, the proximity effect coupling coefficient is extracted. The strength of the proximity effect is quantified by analyzing the mutual inductance between adjacent conductors and the degree of current distribution distortion. The proximity effect coupling coefficient is calculated by comprehensively considering the ratio of the conductor spacing to the grounding grid conductor radius and the excitation frequency. Based on the skin effect depth and proximity effect coupling coefficient, the frequency-varying components of the equivalent resistance at different frequency points are calculated. These components are obtained by integrating the square of the current density over the conductor volume to obtain the power loss, then dividing by the square of the current. The frequency-varying components of the equivalent inductance are also calculated, determined by the ratio of the magnetic field energy to the square of the current. Finally, the real and imaginary parts of the grounding grid's frequency-domain impedance are obtained. The real part of the grounding grid's frequency-domain impedance is equal to the frequency-varying component of the equivalent resistance, and the imaginary part is equal to the product of the excitation frequency and the frequency-varying component of the equivalent inductance.

[0056] The specific implementation of step S05 involves synthesizing the real and imaginary parts of the grounding grid's frequency domain impedance at different frequency points into a complex-form grounding grid frequency response function. The real part of this function corresponds to the real part of the grounding grid's frequency domain impedance, and the imaginary part corresponds to the imaginary part. The magnitude of the grounding grid's frequency response function is calculated, obtained by taking the square root of the sum of the squares of the real and imaginary parts of the grounding grid's frequency domain impedance. The phase characteristic of the grounding grid's impedance is then calculated, obtained by using the arctangent function of the ratio of the imaginary to the real part of the grounding grid's frequency domain impedance. The amplitude-frequency and phase-frequency curves of the grounding grid's frequency response function are plotted. The frequency locations where minimum or maximum values ​​occur on the amplitude-frequency curve are identified; these frequency locations are the resonant frequency distribution locations. At these resonant frequency distribution locations, the inductive and capacitive impedances of the grounding grid cancel each other out, resulting in an extreme value in the total impedance. A mapping relationship is established between the intermediate frequency impulse excitation frequency and the real part and imaginary part of the grounding grid frequency domain impedance. The mapping relationship is stored in the form of a function expression or data table with frequency as the independent variable and impedance as the dependent variable, for use in subsequent time-domain response synthesis.

[0057] The specific implementation of step S06 involves using the convolution theorem to transform the frequency domain response of different narrowband components to the time domain. The frequency domain impedance of each narrowband component is multiplied by the corresponding excitation spectrum amplitude. Then, an inverse fast Fourier transform is used to synthesize all frequency components into a time-domain impulse response waveform. During the synthesis process, the local electric field intensity on the surface of the grounding grid conductor is acquired in real time. The electric field intensity distribution in the soil surrounding the conductor is measured using an electric field probe, and the peak position and amplitude of the electric field intensity are recorded. The peak current density is acquired, determined by the maximum value of the current density vector field distribution on the conductor cross-section. The degree of soil ionization is calculated based on the ratio of the local electric field intensity to the soil breakdown field strength. When the local electric field intensity approaches or exceeds the soil breakdown field strength, the degree of soil ionization increases. The reference value for the soil breakdown field strength is 300 kV / m to 500 kV / m. Soil ionization degree, peak current density, and local electric field strength were normalized to the range of 0 to 1. The normalization method involved subtracting the minimum value from each parameter and dividing by the parameter's range. The normalized soil ionization degree was multiplied by a weighting factor of 0.5, the normalized peak current density by a weighting factor of 0.3, and the normalized local electric field strength by a weighting factor of 0.2. These three values ​​were then added together to obtain the adjustment value. The initial grid density parameter and the iteration convergence accuracy parameter were adjusted based on the range of the adjustment value. When the adjustment value was in the range of 0 to 0.3, it indicated that the soil ionization degree was weak and the current density distribution was relatively uniform. The initial grid density parameter was kept unchanged, and the iteration convergence accuracy parameter remained constant. When the adjustment value is between 0.3 and 0.7, it indicates a moderate degree of soil ionization or an increasing current density gradient. In this case, the initial grid density parameter is increased by 20%, and the number of grid cells is increased in areas with large current density gradients to improve solution accuracy. When the adjustment value is between 0.7 and 1, it indicates a significant degree of soil ionization or a highly non-uniform current density distribution. In this case, the initial grid density parameter is increased by 50%, and the iteration convergence accuracy parameter is reduced to [value missing]. The reliability and accuracy of numerical solutions under strongly nonlinear conditions are ensured by using a denser grid and more stringent convergence criteria.

[0058] It should be noted that one of the key technical ideas of this invention is to use a fractal dimension adaptive mesh generation algorithm to achieve multi-scale refined modeling of the electromagnetic field simulation of grounding grids. Traditional methods use uniform mesh division, which results in a large number of redundant mesh elements in geometrically simple regions and insufficient mesh density in geometrically complex regions, making it impossible to simultaneously guarantee computational accuracy and efficiency. This invention quantifies the spatial complexity of the grounding grid by calculating the box dimension and information dimension of the geometric structure, and adaptively adjusts the mesh density according to the local fractal dimension. This allows computational resources to be concentrated on conductor bends and branch nodes where the current density gradient is large and the electromagnetic field changes drastically, while maintaining a sparse mesh in regions with gentle electric field distribution. Thus, while ensuring the accuracy of current density calculation, the total number of meshes and computation time are significantly reduced, making it particularly suitable for refined electromagnetic field simulation of complex topology grounding grids with a large number of branches and bends.

[0059] The second key technical approach of this invention is to establish an impedance characteristic extraction model based on neural tangent kernel theory to achieve rapid and accurate prediction of grounding grid impedance in the mid-frequency band. While the traditional finite element method is accurate, it is computationally time-consuming and cannot meet the needs of rapid analysis under multiple operating conditions. Traditional neural networks lack theoretical convergence guarantees and suffer from prediction inaccuracies under extrapolation. This invention utilizes the infinite width limit theory of neural tangent kernels to map the training process of deep neural networks into a linear optimization problem of kernel methods. This gives the model strict theoretical convergence guarantees and uncertainty quantification capabilities. Even when faced with grounding grid configurations not fully covered in the training dataset, it can still provide reliable impedance predictions and confidence interval estimates, thereby improving the accuracy and robustness of grounding system performance evaluation under mid-frequency impulse conditions and avoiding the risk of prediction inaccuracies under extrapolation in traditional black-box neural networks.

[0060] The third key technical idea of ​​this invention is to design an adaptive adjustment function to dynamically adjust the grid density parameters and iterative convergence accuracy parameters according to the degree of soil ionization. Traditional methods using fixed grid configurations and convergence criteria cannot adapt to the drastic changes in impedance characteristics caused by strong nonlinear effects such as soil ionization. Under strong ionization conditions, numerical calculations are prone to divergence or insufficient accuracy. This invention calculates the degree of soil ionization by real-time acquisition of local electric field strength and current density peak values. It adaptively increases the grid density and improves the iterative convergence accuracy according to different stages of soil ionization. In the weak ionization stage, it maintains a coarser grid and a looser convergence criterion to improve computational efficiency. In the strong ionization stage, it adopts a denser grid and a stricter convergence criterion to ensure the reliability of the numerical solution, thus achieving a dynamic balance between computational accuracy and efficiency under different ionization levels.

[0061] The synergistic effect of the three key technical approaches lies in the fact that the fractal-dimensional adaptive grid generation algorithm provides a high-quality spatial discretization foundation for the impedance characteristic extraction model, enabling the current density distribution and electromagnetic field distribution in the model training dataset to have higher accuracy and richer multi-scale features, thus enhancing the model's generalization ability. The rapid prediction capability of the impedance characteristic extraction model provides real-time feedback for the adaptive adjustment function, allowing adjustments to the grid density parameter and iterative convergence accuracy parameter to respond promptly to changes in soil ionization. The adaptive adjustment function further enhances the adaptability of the fractal-dimensional adaptive grid generation algorithm under strongly nonlinear conditions through dynamic optimization of the grid configuration. These three approaches form a closed-loop synergistic optimization mechanism, fundamentally resolving the contradiction between insufficient accuracy and low computational efficiency in the extraction of grounding grid impedance characteristics under mid-frequency impulses using traditional methods, and achieving accurate and efficient extraction of the frequency domain impedance characteristics of grounding systems under complex operating conditions.

[0062] It should be noted that this invention also solves the following technical problem: In the analysis of grounding grid impedance characteristics, traditional methods struggle to simultaneously achieve both computational accuracy and efficiency, especially when dealing with complex grounding grid structures containing numerous branches and bends. Uniform grid division results in an excessively large total number of grids and excessively long computation time, or an overly sparse grid leading to insufficient solution accuracy. This invention employs a fractal dimension adaptive grid generation algorithm. Based on the quantization spatial complexity of the box dimension and information dimension of the grounding grid geometry at different observation scales, it uses quadtree and octree data structures to hierarchically manage the grid. At conductor bends and branch nodes, geometric abrupt changes cause a local increase in fractal dimension, triggering automatic grid refinement. In regions with gentle electric field distribution, the smaller fractal dimension maintains a sparse grid. Through recursive subdivision, multi-level grid dynamic generation and optimization are achieved, allowing computational resources to be concentrated in areas of drastic electromagnetic field changes. This significantly reduces the total number of grids and computation time while ensuring the accuracy of current density calculation, resolving the contradiction between insufficient accuracy and excessive computational load in traditional uniform grids when dealing with multi-scale geometric features.

[0063] Specifically, the principle of this invention is as follows: This invention solves the technical problem of accurately extracting the frequency domain impedance characteristics of grounding grids under medium-frequency impulse conditions. Its core principle lies in combining the fractal characteristics of the grounding grid's geometric structure with a grid generation algorithm. By calculating the local fractal dimension to quantify spatial complexity, it achieves adaptive matching between grid density and the intensity of electromagnetic field changes, thereby obtaining a high-precision current density distribution with limited computational resources. Simultaneously, this invention introduces neural tangent kernel theory to establish an impedance characteristic extraction model. Utilizing the equivalence of neural networks to Gaussian processes under the infinite width limit, the nonlinear neural network training process is linearized into a kernel ridge regression problem, enabling the model to possess theoretical interpretability and generalization guarantees when dealing with frequency variations in soil electromagnetic parameters and multi-frequency coupling effects. Furthermore, this invention dynamically adjusts the grid density parameters and iterative convergence accuracy parameters based on the degree of soil ionization, and adaptively optimizes the impedance nonlinearity changes under strong ionization conditions to ensure accurate capture of the frequency domain impedance characteristics of the grounding grid under different working conditions. The logical self-consistency of this technical solution is reflected in the synergy between fractal dimension-driven grid optimization and intelligent prediction supported by neural tangent kernel theory, which together improve the accuracy and robustness of grounding grid impedance characteristic extraction under mid-frequency impulse excitation.

[0064] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0065] The specific implementation of step S01 involves establishing a three-dimensional geometric model of the grounding grid, defining the spatial coordinates of the horizontal and vertical grounding electrodes, collecting the conductor radius, vertical electrode length, and horizontal electrode length, and using a fractal dimension adaptive mesh generation algorithm to divide the conductor region of the grounding grid into meshes. The mesh cells are densified at conductor bends and branch nodes, and sparsed in regions with gentle electric field distribution. (Box dimension) The calculation formula is expressed as follows: ; In the formula, Let the box dimension be 1. For scale Minimum number of boxes required for the under-grounding grid conductor; As a reference scale The number of boxes specified below, defaulting to 1; This is the current side length of the box, in meters (m). For reference, the side length of the box is measured in meters (m), and is typically taken as the maximum span of the grounding grid. Information Dimension The calculation formula is expressed as follows: ; In the formula, For information dimension; For the first Probability measure of grounding grid nodes within a box; The reference probability for a uniform distribution is, empirically, [value]. ; This represents the total number of boxes at the current scale. Box number. Local mesh density. The adjustment formula is expressed as follows: ; In the formula, This is the adjusted grid density, expressed in units of cells per cubic meter. The initial grid density parameter is expressed in units of cells per cubic meter. For local fractal dimensions; The reference fractal dimension is 1.5 by default; The grid density adjustment index is set to 2.0, which is used to obtain the initial grid density parameters.

[0066] The specific implementation of step S02 involves collecting spatial distribution data of soil resistivity and spatial distribution data of soil magnetic permeability in the area where the grounding grid is located, establishing a multilayer soil complex permittivity model, and characterizing the soil permittivity and soil conductivity as functions of frequency. Soil complex permittivity The formula for expressing this is as follows: ; In the formula, The complex permittivity of soil; The relative permittivity of the soil; Soil electrical conductivity, expressed in S / m; The excitation frequency is expressed in Hz. Let be the vacuum permittivity, and take the value of . F / m; The unit is imaginary. Frequency-varying parameter of soil dielectric constant. The following is an expression using the Debye relaxation model: ; In the formula, For frequency The relative permittivity of the soil is as follows; It is the high-frequency limiting dielectric constant, which is usually taken as 5; The static dielectric constant is typically between 20 and 80, and is obtained through experimental measurement. The experimental steps include: Step 1: collecting soil samples and preparing them into standard specimens; Step 2: measuring the dielectric constant of the soil samples under low-frequency conditions using a dielectric constant tester. Let be the relaxation time constant, in seconds, with an empirical value of . to s; The normalized frequency is set to 1 Hz. Soil resistivity frequency variation parameters. The calculation formula is expressed as follows: ; In the formula, For frequency Soil resistivity, in units of ; DC soil resistivity, unit: ; The reference resistivity is set to 1. ; The characteristic frequency is expressed in Hz, with an empirical value of 10kHz. The frequency dependence index is 0.5, and the frequency-dependent parameters of soil resistivity and soil dielectric constant at different depths are obtained.

[0067] The specific implementation of step S03 is to set the frequency range of the intermediate frequency impulse excitation signal to 0.5kHz to 10kHz, decompose the intermediate frequency impulse excitation signal into multiple narrowband components, establish a corresponding frequency domain excitation source for each narrowband component, and input the frequency-varying parameters of the grounding grid conductor radius, vertical grounding body length, horizontal grounding body length, soil resistivity, and soil dielectric constant into the impedance characteristic extraction model. The current density vector field distribution and electromagnetic field distribution inside the grounding grid conductor at different frequency points are calculated through the impedance characteristic extraction model.

[0068] The specific implementation of step S04 is based on solving the spatial variation law of current density across the conductor cross-section of the grounding grid using Maxwell's equations. The skin effect depth and proximity effect coupling coefficient are extracted based on the current density vector field distribution. The equivalent resistance frequency-varying component and equivalent inductance frequency-varying component are then calculated at different frequency points. (Skin effect depth...) The calculation formula is expressed as follows: ; In the formula, The skin effect depth is expressed in meters (m). The excitation frequency is expressed in Hz. The relative permeability of the conductor is 1 for copper conductors; Let be the vacuum permeability, with a value of . H / m; The conductivity of a conductor is expressed in S / m. For copper conductors, the value is [value missing]. S / m. Proximity effect coupling coefficient. The calculation formula is expressed as follows: ; In the formula, The proximity effect coupling coefficient; The radius of the grounding grid conductor is expressed in meters (m). The distance between adjacent conductors, in meters, is extracted from the grounding grid geometric model. The skin effect depth, measured in meters (m). Frequency-dependent component of equivalent resistance. The calculation formula is expressed as follows: ; In the formula, The equivalent resistance frequency-varying component, in units of ; DC resistance, unit is ; The conductor length is expressed in meters (m). For reference length, the value is 1m; This is a proximity effect correction factor, with an empirical value of 0.6. The equivalent inductance frequency-varying component... The calculation formula is expressed as follows: ; In the formula, The equivalent inductance frequency-varying component is expressed in ohms (H). Given the relative permeability of the conductor, obtain the real part and imaginary part of the frequency domain impedance of the grounding grid.

[0069] The specific implementation of step S05 involves constructing the grounding grid frequency response function based on the real and imaginary parts of the grounding grid's frequency domain impedance, identifying the resonant frequency points within the function, and calculating the equivalent impedance magnitude and phase characteristics of the grounding grid. (Grounding grid frequency response function) The formula for expressing this is as follows: ; In the formula, This is the frequency response function of the grounding grid, in units of... ; The real part of the frequency domain impedance of the grounding grid is given by . ; The imaginary part of the frequency domain impedance of the grounding grid, in units of Equivalent impedance modulus of grounding grid The calculation formula is expressed as follows: ; In the formula, The equivalent impedance modulus of the grounding grid, in units of . ; The reference resistor has a value of 1. ; The reference reactance is set to 1. ; The normalized impedance reference is set to 1. Grounding grid impedance phase characteristics The calculation formula is expressed as follows: ; In the formula, To establish the phase characteristics of the grounding grid impedance in rad, a mapping relationship is established between the intermediate frequency impulse excitation frequency and the real and imaginary parts of the grounding grid frequency domain impedance.

[0070] The specific implementation of step S06 involves using the convolution theorem to synthesize the frequency domain responses of different narrowband components into a time-domain impulse response, acquiring the peak values ​​of local electric field strength and current density, calculating the degree of soil ionization, and inputting the soil ionization degree, peak current density, and local electric field strength into an adaptive adjustment function. The adjustment value is then calculated using the adaptive adjustment function. (Soil ionization degree) The calculation formula is expressed as follows: ; In the formula, The degree of soil ionization; This represents the local electric field strength, expressed in V / m. This represents the soil breakdown field strength, expressed in V / m, and is typically taken as a value of [value missing]. to V / m is related to soil moisture and composition; The normalized field strength is set to 1 V / m. The adjustment value output by the adaptive adjustment function is... The calculation formula is expressed as follows: ; In the formula, This is the adjustment value; This represents the maximum degree of ionization, typically set to 1. Peak current density, in A / m ; Maximum current density, in A / m The value is determined based on the current-carrying capacity of the conductor material; copper conductors typically have a value of [value missing]. A / m ; The maximum electric field strength is expressed in V / m, and is taken as the soil breakdown field strength. The initial grid density parameter and the iterative convergence accuracy parameter are adjusted according to the adjustment value. While maintaining the initial mesh density parameter, when the adjustment value Increase the initial mesh density parameter by 20% when adjusting the value. The initial grid density parameter is increased by 50%, and the iteration convergence accuracy parameter is decreased.

[0071] The skin effect depth refers to the depth at which the current density inside a grounding grid conductor decreases exponentially with increasing depth from the surface under high-frequency current. The skin effect depth is inversely proportional to the square root of the excitation frequency and is related to the conductor's resistivity and permeability. In the mid-frequency range, the skin effect causes current to concentrate in a thin layer on the conductor's surface, reducing the effective cross-sectional area and increasing the equivalent resistance. The formula for the current density decay law is as follows: ; In the formula, Depth from conductor surface Current density at a given location, in A / m ; The surface current density of the conductor, expressed in A / m. ; This represents the radial distance from the center of the conductor, expressed in meters (m).

[0072] The resonant frequency distribution location refers to the frequency location where the grounding grid's frequency response function exhibits an extreme value. At the resonant frequency distribution location, the inductive and capacitive impedances of the grounding grid cancel each other out, resulting in a minimum or maximum total impedance. The resonant frequency distribution location is jointly determined by the grounding grid's geometric dimensions and soil electromagnetic parameters. If a resonant frequency distribution location exists within the frequency components included in the mid-frequency impulse excitation, the grounding grid's impedance characteristics will change significantly. Resonant frequency. The estimation formula is expressed as follows: ; In the formula, The resonant frequency is expressed in Hz. The speed of light in a vacuum is given by a value of . m / s; The relative permittivity of the soil; The relative magnetic permeability of the soil is usually taken as 1.

[0073] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the effectiveness of the invention, technicians set up a test environment and analyzed the impedance characteristics of a substation grounding grid under medium-frequency oscillation impact. The grounding grid adopts a grid-type layout structure, with a total horizontal grounding electrode length of 480m, including 12 horizontal conductors, each 40m long, with a conductor spacing of 8m. There are a total of 24 vertical grounding electrodes, each 2.5m long, evenly distributed at the intersections of the horizontal grounding grid. The grounding grid conductors are made of round steel with a radius of 8mm and a burial depth of 0.8m.

[0074] Technicians built a data acquisition system, such as Figure 2As shown, the system mainly consists of an impulse current generator, a high-frequency current sensor, a wideband voltage measurement unit, a soil parameter tester, a multi-channel data acquisition card, and a signal processing workstation. The impulse current generator can produce mid-frequency oscillating impulse signals covering a frequency range of 0.5kHz to 10kHz, with a peak current of up to 500A. The high-frequency current sensor uses a Rogowski coil structure, with a bandwidth of 0.1kHz to 200kHz and a sensitivity of 10mV / A. The wideband voltage measurement unit is based on differential probe technology, with an input impedance greater than 10Ω. The frequency response range is from DC to 150kHz. The soil parameter tester can measure soil resistivity and dielectric constant at different depths, with a measurement frequency range of 50Hz to 100kHz. The multi-channel data acquisition card has 8 synchronous sampling channels, a sampling rate of 2MS / s, and a resolution of 16 bits. The signal processing workstation is equipped with an Intel i7 processor and 32GB of memory, running MATLAB and Python environments for data processing and analysis.

[0075] Technicians first used a soil parameter tester to measure the soil resistivity in the area where the grounding grid was located, employing the Wenner four-electrode method at different depths. The measurement results showed that the soil in this area exhibited a clear horizontal stratification characteristic, with a soil resistivity of 85 ohms in the top layer from 0 to 1.2 meters. The soil resistivity in the middle layer, at a depth of 1.2 to 3.5 m, is 152 ppm. The soil resistivity below 3.5m is 220 kJ / m². The dielectric constant of soil at different frequencies was obtained through frequency domain dielectric spectroscopy. The relative dielectric constant of the surface soil was 12.5 at 1 kHz, decreasing to 8.3 at 50 kHz, which conforms to the dispersion characteristics of the Debye relaxation model. Based on the measurement data, the technicians established a multilayer soil complex dielectric constant model, characterizing the real part of the soil dielectric constant and the imaginary part of the conductivity as functions of frequency.

[0076] Subsequently, technicians established a three-dimensional geometric model of the grounding grid and used a fractal dimension adaptive mesh generation algorithm to divide the conductor region of the grounding grid into meshes. The calculated box dimension of the grounding grid conductor at different scales was 1.68, and the information dimension was 1.52, reflecting the complexity and non-uniformity of the spatial distribution of the grounding grid. At conductor bends and branch nodes connecting vertical and horizontal grounding electrodes, the fractal dimension locally reached 2.1, triggering automatic mesh refinement, with the mesh cell size refined to 5mm. In soil regions far from the conductor, the fractal dimension decreased to 0.8, maintaining a sparse mesh with a cell size of 200mm. The final generated adaptive mesh contained 1.26 million cells, a 58% reduction in the number of cells compared to a traditional uniform mesh.

[0077] Technicians set the mid-frequency impulse excitation signal as a damped oscillating waveform with a dominant frequency of 25kHz, a decay time constant of 80μs, and a peak current of 350A. This impulse signal was decomposed into 128 narrowband components using a Fast Fourier Transform, with a frequency interval of 781Hz, covering a range from 0.5kHz to 10kHz. A corresponding frequency domain excitation source was established for each narrowband component, and models were extracted from the grounding grid geometric parameters, soil electromagnetic parameters, and input impedance characteristics at the excitation frequency. This model employs a three-layer hidden layer structure: the first hidden layer contains 128 neurons for extracting the spatial topological features of the grounding grid; the second hidden layer contains 256 neurons for fusing soil parameters and frequency information; and the third hidden layer contains 128 neurons for constructing a high-dimensional representation of the impedance characteristics. The model training dataset contains 1500 electromagnetic field simulation samples under different working conditions, covering soil resistivity from 10 to 1000 Ω·cm. The parameters are defined as follows: conductor radius 5 to 20 mm, vertical grounding electrode length 1 to 10 m. The Xavier initialization method is used to initialize the network weights, and the Adam optimizer is used for training. The learning rate is set to 0.001, the batch size is 32, and after 185 iterations, the validation set loss converges to 0.0034.

[0078] Technicians calculated the current density vector field distribution and electromagnetic field distribution inside the grounding grid conductor at different frequencies using an impedance characteristic extraction model. At 5 kHz, the skin effect depth was 18.7 mm, and the current distribution was relatively uniform. As the frequency increased to 50 kHz, the skin effect depth decreased to 5.9 mm, and the current concentrated in a thin layer on the conductor surface, significantly reducing the effective conductive cross-sectional area. For adjacent parallel horizontal conductors with a spacing of 8 m, the proximity effect coupling coefficient was 0.23 at 50 kHz. Electromagnetic coupling between adjacent conductors caused current distribution distortion, resulting in an approximately 15% increase in current density on the side facing the adjacent conductor.

[0079] Based on Maxwell's equations, the spatial variation of current density across the conductor cross-section of the grounding grid was determined. Technicians extracted the frequency-varying components of the equivalent resistance and equivalent inductance at different frequencies. At 1 kHz, the equivalent resistance of the grounding grid was 0.38... The resistance is close to 0.35 ohms (DC resistance value). As the frequency increases to 20kHz, the equivalent resistance increases to 0.67. The increase reached 76%. At 50kHz, the equivalent resistance further increased to 1.15. The increase reached 229%. The equivalent inductance was 8.5 μH in the low-frequency range, and showed a slow decreasing trend with increasing frequency, dropping to 7.1 μH at 50 kHz, a decrease of 16%. The calculation results are shown in Table 1.

[0080] Table 1. Grounding grid impedance parameters at different frequencies

[0081] Technicians constructed the frequency response function of the grounding grid based on the real and imaginary parts of its frequency domain impedance, such as... Figure 3 As shown, the magnitude of the frequency response function increases slowly in the low-frequency range, with two distinct resonant peaks at 23kHz and 67kHz, where the impedance magnitudes reach 2.3. and 3.1 An anti-resonance trough appears at 38kHz, and the impedance modulus drops to 0.9. The phase characteristic curve shows a dramatic phase change near the resonant frequency point. At the 23kHz resonant point, the phase angle jumps from 15 degrees to -28 degrees, indicating that the impedance characteristic changes from inductive to capacitive. These resonant frequencies are determined by the geometry of the grounding grid and the electromagnetic parameters of the soil, and are related to the quarter-wavelength resonant characteristic corresponding to the length of the horizontal conductor of the grounding grid.

[0082] By using the convolution theorem to synthesize the frequency domain responses of different narrowband components into a time-domain impulse response, technicians obtained the time-domain waveforms of the voltage and current at the grounding grid injection point, such as... Figure 4 As shown. At the peak of the impulse current, the grounding grid potential rises to 425V, corresponding to an instantaneous impedance of 1.21V. Due to the resonance effect, the voltage waveform exhibits a significant oscillation attenuation characteristic, with the oscillation frequency mainly concentrated around 23kHz. By extracting the envelopes from the voltage and current waveforms using Hilbert transform, it was found that the voltage envelope attenuation time constant is 65μs, which is faster than the current envelope attenuation time constant of 80μs, reflecting the frequency dependence of the grounding grid impedance.

[0083] Technicians collected data on the local electric field intensity distribution on the surface of the grounding grid conductor and the surrounding soil. At the branch node region where the vertical and horizontal grounding electrodes connect, the peak local electric field intensity reached 18.5 kV / m. At the bend in the horizontal conductor, the peak electric field intensity was 12.3 kV / m. Based on the measured soil breakdown field strength of 25 kV / m, the soil ionization degree at the branch node was calculated to be 0.74, and at the bend, it was 0.49. The peak current density at the branch node reached [data missing]. At the bend Technicians input these parameters into the adaptive adjustment function; the adjustment value for the branch node region was calculated to be 0.68, and the adjustment value for the bend was 0.42. Figure 5 As shown.

[0084] Based on the adjustment values, technicians adaptively adjusted the mesh density and iterative convergence accuracy. For branch node regions with an adjustment value of 0.68, the initial mesh density parameter was increased from 20 elements per cubic centimeter to 24 elements per cubic centimeter, an increase of 20%. For bends with an adjustment value of 0.42, the mesh density parameter was also increased by 20%. In a few extreme ionization regions where the adjustment value exceeded 0.7, the mesh density parameter was increased by 50%, and the iterative convergence accuracy parameter was adjusted from... Reduce to To ensure the reliability of the numerical solution under strong ionization conditions, the recalculated grounding grid impedance characteristics, after adjustment, show that considering the soil ionization effect, the peak impulse impedance decreases from 1.21... Reduced to 0.95 The decrease was 21%, which more accurately reflects the performance of the grounding grid under actual working conditions.

[0085] The advancement of this invention over traditional methods lies in its intelligent allocation of computational resources through a fractal dimension adaptive mesh generation algorithm, avoiding the contradiction of insufficient accuracy or excessive computational load in traditional uniform meshes when handling complex geometric features. The impedance characteristic extraction model based on neural tangent kernel theory establishes a theoretical connection between deep learning and kernel methods, enabling the model to provide reliable predictions and uncertainty estimates even when facing conditions not fully covered by training data, overcoming the shortcomings of insufficient extrapolation capabilities in traditional black-box neural networks. The multilayer soil complex dielectric constant model accurately describes the frequency dispersion characteristics of soil electromagnetic parameters, reflecting the dielectric response of soil in the mid-frequency range more realistically than traditional constant parameter models. The adaptive adjustment mechanism dynamically optimizes mesh density and convergence accuracy according to the degree of soil ionization, solving the problem of insufficient accuracy of traditional fixed parameter methods under strong ionization conditions, and significantly improving the accuracy and robustness of grounding system performance evaluation under mid-frequency impulse conditions.

[0086] It should be noted that the variables involved in this invention are explained in detail in Table 2.

[0087] Table 2 Variable Explanation Table

[0088] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for extracting the frequency domain impedance characteristics of a grounding grid under medium-frequency oscillation impulse, characterized in that, Includes the following steps: A three-dimensional geometric model of the grounding grid was established, and the spatial coordinates of the horizontal and vertical grounding electrodes were defined. The conductor radius, vertical electrode length, and horizontal electrode length of the grounding grid were collected. A fractal dimension adaptive mesh generation algorithm was used to divide the conductor region of the grounding grid into meshes, obtaining initial mesh density parameters. Spatial distribution data of soil resistivity and permeability in the grounding grid area were collected, and a multi-layer soil complex dielectric constant model was established to obtain the frequency-varying parameters of soil resistivity and dielectric constant at different depths. The frequency range of the intermediate-frequency impulse excitation signal was set to 0.5kHz to 10kHz. The intermediate-frequency impulse excitation signal was decomposed into multiple narrowband components. The conductor radius, vertical electrode length, horizontal electrode length, soil resistivity frequency-varying parameters, and soil dielectric constant frequency-varying parameters were input into the impedance characteristic extraction model. The impedance characteristic extraction model was used to calculate the values ​​at different frequency points. The current density vector field distribution and electromagnetic field distribution inside the grounding grid conductor are determined. Based on Maxwell's equations, the spatial variation law of current density in the cross section of the grounding grid conductor is solved. The skin effect depth and proximity effect coupling coefficient are extracted based on the current density vector field distribution. The frequency-varying components of equivalent resistance and equivalent inductance at different frequency points are calculated, and the real and imaginary parts of the grounding grid frequency domain impedance are obtained. The frequency response function of the grounding grid is constructed based on the real and imaginary parts of the grounding grid frequency domain impedance, and the distribution location of the resonant frequency points in the frequency response function is identified. The frequency domain responses of different narrowband components are synthesized into a time-domain impulse response using the convolution theorem. The local electric field strength and current density peak values ​​are collected, and the soil ionization degree is calculated. The soil ionization degree, current density peak value, and local electric field strength are input into an adaptive adjustment function, and the initial grid density parameters and iterative convergence accuracy parameters are adjusted according to the adjustment value.

2. The method according to claim 1, characterized in that, The fractal dimension adaptive grid generation algorithm densifies the grid cells at conductor bends and branch nodes, and sparses the grid cells in regions with gentle electric field distribution. It quantifies the spatial complexity by calculating the box dimension and information dimension of the grounding grid geometry at different observation scales.

3. The method according to claim 2, characterized in that, The box dimension reflects the filling characteristics of the grounding grid conductor in space, and the information dimension reflects the non-uniformity of the distribution of grounding grid nodes. The degree of grid densification in a region is automatically determined based on the magnitude of the local fractal dimension value.

4. The method according to claim 3, characterized in that, The fractal dimension adaptive mesh generation algorithm uses a quadtree data structure to hierarchically manage the two-dimensional cross-sectional mesh and an octree data structure to hierarchically manage the three-dimensional spatial mesh. It achieves dynamic generation and optimization of multi-level meshes through recursive subdivision.

5. The method according to claim 4, characterized in that, The specific implementation steps of the fractal dimension adaptive mesh generation algorithm include: projecting the three-dimensional geometric model of the grounding grid onto the horizontal and vertical planes, covering the grounding grid conductor with cubic boxes of decreasing side lengths at different scales, counting the minimum number of boxes required at each scale, and calculating the box dimension by the slope of the minimum number of boxes and the box scale in the double logarithmic coordinate system.

6. The method according to claim 5, characterized in that, The fractal dimension adaptive grid generation algorithm assigns a probability measure to each node of the grounding grid to characterize the concentration of current distribution, calculates the information dimension to quantify the non-uniformity of node distribution, and recursively subdivides the coarse grid cells into quadtrees or octrees when the fractal dimension exceeds a set threshold.

7. The method according to claim 6, characterized in that, The multilayer soil complex dielectric constant model characterizes the soil dielectric constant and soil conductivity as functions of frequency, and represents the electromagnetic properties of soil as a frequency-dependent complex number. The real part of the complex dielectric constant corresponds to the soil dielectric constant, and the imaginary part of the complex dielectric constant corresponds to the ratio of soil conductivity to frequency.

8. The method according to claim 7, characterized in that, The multilayer soil complex dielectric constant model describes the dispersion characteristics of soil dielectric constant with frequency using the Debye relaxation model or the Cole-Cole model.

9. The method according to claim 8, characterized in that, For each narrowband component, a corresponding frequency domain excitation source is established. The impedance characteristic extraction model utilizes the connection between the infinite width limit theory based on the neural tangent kernel and the Gaussian process. By analyzing the neural network as equivalent to the kernel method under infinite width, the neural tangent kernel is used for theoretical analysis and uncertainty quantification.

10. The method according to claim 9, characterized in that, The specific structure of the impedance characteristic extraction model is as follows: the input layer receives the conductor radius of the grounding grid, the length of the vertical grounding body, the length of the horizontal grounding body, the frequency-varying parameters of soil resistivity and soil dielectric constant, and the excitation frequency; feature extraction and nonlinear mapping are performed through three hidden layers; and the output layer outputs the real part of the frequency domain impedance of the grounding grid, the imaginary part of the frequency domain impedance of the grounding grid, and the current density distribution correction coefficient.

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